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| 1.
Answer E |
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| 2.
Answer D |
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| 3.
Answer E |
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| 4.
Answer D |
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| 5. 
Answer D |
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6.
Answer C |
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| 7. Creating a sign study of f ' and what
it tells you about f:
Answer B |
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| 8.
Answer B |
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| 9.
Answer A |
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| 10. If f(x) < 0 for all x, then the y
values are all negative for all x. If f '(x) < 0 for all x, then f is
decreasing for all x.
If f " (x) < 0 for all x, then f is concave down for all x.
Graph B has all these qualities.
Answer B |
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| 11.
Answer C |
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| 12.
Answer E |
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| 13. At point a the graph is continuous,
but not differentiable because the limit of the difference quotient for
slopes does not exist at this point. Answer A |
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| 14.
Answer E |
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| 15.
 yields the following
sign study for f '.
where a = 0 and b= .negative
From the sign study we can see that f ' is negative in the interval
 and this is where f is
decreasing.
Answer D |
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| 16.
The derivative at x
= 1 is equal to the slope of the tangent line at x = 1. The line
passes through (1, 7) and (-2, -2) so the slope is
The tangent line has a slope of 3 so this is the slope of the function f
at -1.
Answer C |
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| 17.
Answer A |
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| 18. g ' has exactly 2 zeros at x = -2 and
x = 2.
g is increasing (-∞, -2) and (2,∞) because g ' is positive in these
intervals. g is decreasing on (-2,2)
because g ' is negative on this interval.
Answer A |
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| 19. f ' (x)=2x+3 and f(1)=2
Answer D |
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| 20.
I.  so this is
true.
II. In addition to I we also know that f(3)=5 so f is continuous
and this statement is true.
III.  so f is
not differentiable at 3.
So I and II are true.
ANSWER D |
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21.
based on the sign study of f " the second derivative of f changes sign at x
= o and a.
Answer A |
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| 22. The graph f ' is a graph of a linear
function. So f is a quadratic function.
y '=-6x+6 from the information in the graph. So
Answer D
If f(0)=5 we also know that f '(0) = 6 from the graph. So the
equation of y = |
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| 23.
Answer E
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24.
Answer C |
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| 25.
Answer E |
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| 26.
Answer B |
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| 27.
Answer B |
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| 28. g'(x)>0 for all x means g is always increasing
g"(x)>0 for all x means g is always concave up
The green line shows a linear function that is increasing and the blue
curve show a function that is increasing that is concave up.
The equation of the linear function between (4,12) and (5,18) is
y=6(x-4)+12.
y(6)=24 which is the value along the linear function. We know that the value of g(6) must be greater than the
value of y(6).
Answer E.
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